数学季刊

Characterizations of Stable Functions on L-dom ains

陈仪香

1998, 13(1): 1-7.

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In this paper,the author studies the characteristic properties of stable functions between L domains. A basic notion of stable open subsets of L domain is introduced. The author shows that the two element L domains θ={0,1} is the classifier of the category of L domains and stable functions.

Nonlinear Programming Algorithm and Its Convergence Rate Analysis

王国富, 李学全

1998, 13(1): 8-13.

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In this paper,we improve the algorithm proposed by T.F.Colemen and A.R.Conn in paper [1]. It is shown that the improved algorithm is possessed of global convergence and under some conditions it can obtain locally supperlinear convergence which is not possessed by the original algorithm. 专辑：基础科学专题：数学分类号： O221

Hamilton Properties of Domination Critical Graphs

段广森, 王新社

1998, 13(1): 14-21.

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Ewa·Wojcicka [1] has proved that the connected 3 γ critical graphs has a H path and has put forward to such a conjecture: Connected 3 γ critical graphs without endpoints are H graphs. In this paper,we prove that if G is a connected 3 γ critical graph without endpoints and has a Hpaht ap →a such that d(a,b)=3, then G is a H graph. The result partially solves Ewa. Wojcicka's conjecture. 专辑：基础科学专题：数学分类号： O157.5

Asymptotic Behavior of Nodal Solutions for Semilinear Elliptic Equationsin Rⁿ

綦建刚, 刘衍胜

1998, 13(1): 22-28.

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In this paper,we have investigated the asymptotic behavior of nodal solutions of semilinear elliptic equations in Rⁿ. We conclude more precise and extensive results and give the expression of asymptotic behavior near ∞ more detail than that of [3]-[5]. 专辑：基础科学专题：数学分类号： O175

A New Class of Generalized Landau Linear Positive Operator Sequence and Its Properties of Approximation

陈湛本, 石济民

1998, 13(1): 29-43.

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In this paper two sequences of generalized Landau linear positive operators are introduced. They can be applied in approximating continuous functions with arbitrary growth order, defined on a finite interval or the whole real axis. The properties of approximation are studied and their asymptotic formulae are presented. These results show that their degrees of approximation are the best among existing operator sequences of Landau type, for example, their degrees of approximation for C²[0, 1] are O(1/n²) but corresponding degree of ordinary Landau operators are only O(1/n).

A Direct Method for the Problem of the Solid Cylinder in Elasticity

徐新生, 张洪武, 钟万勰

1998, 13(1): 44-54.

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The traditional semi inverse solution method of the Saint Venant problem and the Saint Venant principle,which were described in the Euclidian space under the Lagrange system formulation,are updated to be solved in the symplectic space under the conservative Hamiltonian system. Thus,the Saint Venant problem and the Saint Venant principle have been unified by the direct method. It is proved in the present paper that all the Saint Venant solutions can be obtained directly via the zero eigenvalue solutions and all their Jordan normal form of the corresponding Hamiltonian operator matrix and the Saint Venant principle corresponds to neglect the non zero eigenvalue solutions,where the non zero eigenvalues give the decay rates.

The Degree Theory of a New Operator

闫宝强

1998, 13(1): 55-60.

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This paper defines a concept of a semi k set contract operator and establishes a degree theory for it.

Equicontinuous Seton Locally Convex Spaces

武俊德, 曲文波

1998, 13(1): 61-63.

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Let (E,γ) be a locally convex space and E′ its conjugate space. AE′ be an equicontinuous set on (E,γ). In this paper,we show that for each sequence ... If (E,γ) is metrizable, then we can show that the converse is also valid.

Stability of a Chem ostatModelfor a Single Specieswith Delayed NutrientRecycling——Case ofWeak KernelFunction

蒋里强, 马知恩

1998, 13(1): 64-69.

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In this paper,we study the global stability of the equilibrium in a chemostat model with delayed nutrient recycling by constructing a new Liapunov functional. The Liapunov function is different from the general one adopted in discussing the stability of the of the chemostat model.

Angles of Norm ed Linear Spaces and Characterizations of Inner Product Spaces

郑永爱

1998, 13(1): 70-73.

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In [1],a family of angles are defined in normed linear spaces. In this paper,it is shown that if anyone of the angles satisfies certain euclidean triangle congruence properties,the space must be an inner product space.

The Problem of Periodic Solution for Dynam icalSystem s (Ⅱ)

杨巍纳, 林恒强

1998, 13(1): 74-76.

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In this paper,we consider the dynamical system which are from general Hemilton systems under a disturbance,we use theories in Liapunov stability and show that there are not any periodic solutions in some a neighborhood of the equilibrium points of the dynamical systems.

Extensions of Modules over Commutative Group Algebras

陈焕艮

1998, 13(1): 77-83.

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Let R be a commutative ring with an identity element, G a finitely generated abelian group. In this paper,we investigate necessary and sufficient conditions on G and R such that every finitely generated projective RG module can be extended from R.

Quasi-uniformitieson Lattice Implication Algebras

田英培, 徐扬

1998, 13(1): 84-86.

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We define a quasi uniformity on a lattice H implication algebra. We also introduce a quasi uniformity on any lattice implication algebra by using the set of filters.

The Algebraic Criteria for the All┐delay Stability of Two┐dimensional Degenerate Differential Systems with Delay

蒋威, 郑祖庥

1998, 13(1): 87-93.

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This paper give the algebraic criteria for all delay stability of two-dimensional degenerate differential systems with delays and give two examples to illustrate the use of them．

The Coset Group and Com ove Group

林楠

1998, 13(1): 94-97.

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Based on the concepts of set value map and power group,the definitions of comove relation,coset group and comove group were given,their properties were discussed and meaningful results were obtained.

ω₁-Ordinal Definable Sets and Chang's Model C

赵希顺, 王驹

1998, 13(1): 98-106.

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In this paper，we first introduce the notions of ω₁-ordinal definable sets and hereditarily ω₁-ordinal definable sets．Then we present some properties of the universe HOD₁ of hereditarily ω₁-ordinal definable sets．Finally，using forcing method，we reveal some consistent relationship between HOD₁ and Changʾs model C．

On Theorem of the “Mountain Impasse” Type

张宪君, 戚桂杰

1998, 13(1): 107-110.

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In this paper to the theorem of the “Mountain Impasse” Type given by K.Tintarev,we consider the condition: the state of that “for every p∈Φ _∞, max ξ∈K G(p(ξ)) is attained at some point in K\K *” is relaxed from c(R)>c 0.

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